Stem cells, through their ability to produce daughter stem cells and differentiate into specialized cells, are essential in the growth, maintenance, and repair of biological tissues. Understanding the dynamics of cell populations in the proliferation process not only uncovers proliferative properties of stem cells, but also offers insight into tissue development under both normal conditions and pathological disruption. In this paper, we develop a continuous time branching process model with time-dependent offspring distribution to characterize stem cell proliferation process. We derive analytical expressions for mean, variance, and autocovariance of the stem cell counts, and develop likelihood-based inference procedures to estimate model parameters. Particularly, we construct a forward algorithm likelihood to handle situations when some cell types cannot be directly observed. Simulation results demonstrate that our estimation method recovers the time-dependent division probabilities with good accuracy.

翻译：干细胞通过其产生子代干细胞并分化为特化细胞的能力，在生物组织的生长、维持和修复中起着至关重要的作用。理解增殖过程中细胞群体的动态变化，不仅揭示了干细胞的增殖特性，还为正常条件和病理破坏下的组织发育提供了深入见解。本文提出了一种具有时间依赖性后代分布的连续时间分支过程模型，用以表征干细胞增殖过程。我们推导了干细胞数量的均值、方差和自协方差的解析表达式，并建立了基于似然的推断程序来估计模型参数。特别地，我们构建了一种前向算法似然，以处理某些细胞类型无法直接观测的情况。仿真结果表明，我们的估计方法能够以较高的精度恢复时间依赖性的分裂概率。